A charged particle in a uniform field B moves on a circle in the plane perpendicular to B. Lorentz force = centripetal force gives pT [GeV/c] = 0.3 · B [T] · R [m]. The sign of the bend gives the charge sign.

The tracker only records hits at radii r = 1.4, 2.8, 4.2 m. A circle through three hits has curvature κ = 1/R; for equally spaced layers (spacing h) and a gentle bend, κ ≈ (y1 − 2y2 + y3)/h², so hit noise σ gives σκ = √6 σ / h² and σ(pT)/pT = √6 σ R / h² ∝ pT: stiff tracks are measured worse, which is why real detectors use strong fields and many layers.

The longitudinal part follows z = (p_z/p_T)·s along the arc length s; pseudorapidity η = asinh(p_z/p_T). Simplifications: uniform field, no multiple scattering, no energy loss, only three layers, Gaussian isotropic hit noise, analytic formula valid for R >> h.